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Transcript of © T Madas 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23.
© T Madas
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© T Madas
Polygons with a ruler and a protractor0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
© T Madas
Drawing a Hexagon using a protractor
© T Madas
A hexagon has 6 sidesWe are going to construct 6 equal angles around a point
How many degrees are there around a point?
How many degrees each of these angles must be?
Drawing a Hexagon using a protractor
© T Madas
Drawing a Hexagon using a protractor
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•Start by drawing a circle.•The hexagon will be inscribed in the circle.•The bigger the circle the bigger the hexagon•Mark a horizontal line from the centre
© T Madas
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Drawing a Hexagon using a protractor
© T Madas
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Drawing a Hexagon using a protractor
© T Madas
Drawing a Hexagon using a protractor
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Drawing a Hexagon using a protractor
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Drawing a Hexagon using a protractor
© T Madas
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Drawing a Hexagon using a protractor
© T Madas
Drawing a Hexagon using a protractor
© T Madas
60°
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60°8 cm 8 cm
8 c
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8 cm
Drawing a Hexagon using a protractor
© T Madas
Drawing an Octagon using a protractor
© T Madas
An Octagon has 8 sidesWe are going to construct 8 equal angles around a point
How many degrees are there around a point?
How many degrees each of these angles must be?
Drawing an Octagon using a protractor
© T Madas
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Drawing an Octagon using a protractor•Start by drawing a circle.
•The octagon will be inscribed in the circle.•The bigger the circle the bigger the octagon•Mark a horizontal line from the centre
© T Madas
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Drawing an Octagon using a protractor
© T Madas
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© T Madas
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Drawing an Octagon using a protractor
© T Madas
Drawing an Octagon using a protractor
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Drawing an Octagon using a protractor
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Drawing an Octagon using a protractor
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Drawing an Octagon using a protractor
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Drawing an Octagon using a protractor
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Drawing an Octagon using a protractor
© T Madas
Drawing an Octagon using a protractor
© T Madas
6 cm
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Drawing an Octagon using a protractor
© T Madas
Drawing a Pentagon using a protractor
© T Madas
Drawing a Pentagon using a protractor
A pentagon has 5 sidesWe are going to construct 5 equal angles around a point
How many degrees are there around a point?
How many degrees each of these angles must be?
© T Madas
Drawing a Pentagon using a protractor
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•Start by drawing a circle.•The pentagon will be inscribed in the circle.•The bigger the circle the bigger the pentagon•Mark a horizontal line from the centre
© T Madas
Drawing a Pentagon using a protractor
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© T Madas
Drawing a Pentagon using a protractor
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Drawing a Pentagon using a protractor
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© T Madas
Drawing a Pentagon using a protractor
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Drawing a Pentagon using a protractor
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Drawing a Pentagon using a protractor
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Drawing a Pentagon using a protractor
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© T Madas
Drawing a Pentagon using a protractor
© T Madas
Drawing a Pentagon using a protractor
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© T Madas
Drawing an Enneagon using a protractor
© T Madas
Drawing an Enneagon using a protractor
An Enneagon has 9 sides[It is also called a nonagon but enneagon is its proper name]
We are going to construct 9 equal angles around a point
How many degrees are there around a point?
How many degrees each of these angles must be?
© T Madas
Drawing an Enneagon using a protractor
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•Start by drawing a circle.•The enneagon will be inscribed in the circle.•The bigger the circle the bigger the enneagon•Mark a horizontal line from the centre
© T Madas
Drawing an Enneagon using a protractor
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Drawing an Enneagon using a protractor
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Drawing an Enneagon using a protractor
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© T Madas
Drawing an Enneagon using a protractor
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Drawing an Enneagon using a protractor
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Drawing an Enneagon using a protractor
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Drawing an Enneagon using a protractor
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© T Madas
Drawing an Enneagon using a protractor
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Drawing an Enneagon using a protractor
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Drawing an Enneagon using a protractor
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© T Madas
Drawing an Enneagon using a protractor
© T Madas
Drawing an Enneagon using a protractor
40°
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40°
7 cm
7 cm7 c
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7 cm
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© T Madas
Polygons with Compasses and Straightedge0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
© T Madas
Constructing Regular
Hexagons
© T Madas
Constructing a Regular Hexagon
Why does it work?
© T Madas
Constructing a Regular Hexagon
Why does it work?
© T Madas
Constructing a Regular Hexagon
Why does it work?
© T Madas
Constructing Regular
Pentagons
© T Madas
•Start with the circumscribing circle
•Draw a diameter
•Draw the perpendicular bisector of that diameter
•Mark its intersection with the circle
•Bisect the radius as shown
•Draw arc as shown and mark its intersection with the diameter
•This is the required side length for a regular pentagon, which is circumscribed by the circle
Constructing a Regular Pentagon
© T Madas
Constructing Regular
Octagons
© T Madas
Constructing a Regular Octagon
© T Madas
Constructing Regular
Decagons
© T Madas
•To construct a decagon you need a regular pentagon first
•Bisect one of the sides of the pentagon
•Use the chord of the new arc produced to construct a regular decagon
•You can use this idea to constuct a dodecagon from a hexagon
•A 16 – sided regular polygon using an octagon
•An eicosagon from a decagon and so on
Constructing a Regular Decagon
© T Madas
